Soliton transmission system having plural sliding-frequency guiding filter groups

ABSTRACT

Timing jitter problems are effectively eliminated in a soliton transmission system realized by deploying a series of optical filters in groups whose group average center frequency intentionally differs from the group average center frequency of other optical filter groups. The center frequency of the series of optical filter groups is translated along the desired length of the system in a predetermined manner such as frequency increasing, frequency decreasing, and combinations of both. This creates a transmission environment which is substantially opaque to noise while remaining perfectly transparent to solitons. By arranging the optical filters in groups, it is possible to simplify the system design by reducing the number of filters having different nominal center frequencies.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to allowed, commonly assigned and co-pendingU.S. patent application Ser. No. 07/904,239 (Gordon-Mollenauer Case5-23) filed Jun. 25, 1992.

TECHNICAL FIELD

This invention relates to lightwave transmission systems and, moreparticularly, to such systems wherein optical filters are positioned atspecific locations along the transmission medium of the lightwavesystem.

BACKGROUND OF THE INVENTION

Soliton transmission systems can potentially provide exceedingly highinformation transmission capacity over long distances. In ultra-longdistance systems such as transcontinental and transoceanic systems,optical amplifiers periodically boost the power of propagatinginformation-bearing soliton pulses sufficiently high to compensate forlosses experienced in the fiber transmission medium. Unfortunately forultra-long distance systems, however, the maximum information bit ratefor a single channel is set by the amount of jitter in pulse arrivaltimes generated by two different effects. One is the Gordon-Haus effectand the other is an acoustic interaction effect.

The Gordon-Haus effect is occasioned by the interaction of solitonpulses with amplifier spontaneous emission noise present along thetransmission medium. J. P. Gordon et al. describe this effect in OpticLetters, Vol. 11, No. 10, pp. 665-7 (1986). Amplifier spontaneousemission noise alters both the amplitude and carrier or channelfrequency of the soliton pulses at random resulting in a jitter in pulsearrival times. Pulse jitter can cause a soliton pulse to walk off intothe time interval reserved for a neighboring soliton pulse. The result,often known as intersymbol interference, is an error in the receivedinformation.

M. Nakazawa et al. have suggested in Electronics Letters, Vol. 27, p.1270 (1991) that active electronic devices such as modulators to providetime domain filtering could be used to eliminate soliton pulse arrivaltime jitter. This technique is not only costly, complex, and difficultto implement but it also suffers the same incompatibility withwavelength-division-multiplexing experienced by electronic regenerationof optical signals.

A simpler alternative for reducing jitter from the Gordon-Haus effectwas described in U.S. Pat. No. 5,140,656 issued to Hasegawa et al. anddisclosed in articles by Y. Kodama et al. in Optics Letters, Vol. 17,No. 1, pp. 31-3 (1992) and by A. Mecozzi et al. in Optics Letters, Vol.16, No. 23, pp. 1841-3 (1991). These references propose the use oflinear narrow-band filters (called "frequency guiding filters") spacedat regular predetermined intervals along the transmission fiber. Eachfilter, in essence, shapes the frequency dependent gain characteristicof the corresponding amplifier. The linear filters are effectivelyidentical within manufacturing tolerances in that each filter exhibits acenter frequency substantially equal to the soliton center frequency.However, the introduction of filters causes additional soliton pulseenergy loss which, in turn, must be offset by higher gain from theoptical amplifiers. This higher gain, however, results in an exponentialincrease with increasing distance of those spectral components of thenoise at, or near, the filter response peak. As a result, the maximumusable filter strength is limited as is the amount of realizable jitterreduction. A recent experiment using the frequency guiding filters wasreported by L. Mollenauer et al. in Electronics Letters, Vol. 28, p. 792(1992) for a 10,000 km soliton transmission system in which the filterachieving the lowest bit error rate caused a 50% reduction in thestandard deviation of the timing jitter.

SUMMARY OF THE INVENTION

Timing jitter problems are greatly reduced in a soliton transmissionsystem by deploying a series of optical filters whose center frequenciesintentionally differ from one another, or from a a predeterminedreference frequency, by a varying amount. For example, the centerfrequency of any particular filter differs from the center frequency ofthe adjacent optical filters. The center frequency of the series ofoptical filters is translated toward a desired frequency--giving rise tothe newly coined term "sliding-frequency guiding filter"--along thedesired length of the system in a predetermined manner such as frequencyincreasing, frequency decreasing, and combinations of both. This createsa transmission environment which is substantially opaque to noise whileremaining perfectly transparent to solitons. As a result, strongerfilter response characteristics can be used to achieve greater jitterreduction than prior art systems. In this system, the use of strongerfilter response characteristics does not incur the usual penalty ofexponentially rising noise from the excess amplifier gain required toovercome the additional filter loss.

In this new transmission system, solitons are launched at a particularfrequency Ω and are accelerated toward each successively differentcenter frequency ω_(f),n (n=1, 2, . . . N) in the series ofsliding-frequency guiding filters thereby causing each soliton to emergeat a remote end of the transmission system at a substantially differentfrequency from the launch frequency.

In an improvement over the proposed soliton transmission system above, Ihave discovered that the new system can be further simplified and thenumber of different filter center frequencies can be reduced withoutimpairing the transmission environment which is substantially opaque tonoise while remaining transparent to the solitons. Specifically, thesystem including N×L optical filters will have N consecutive opticalfilters designated to one particular filter group. L such filter groupsare then formed along the transmission system. Filters in each filtergroup combine to have a group average center frequency. The groupaverage center frequency for one group differs from the group averagecenter frequency for every other group along the system. Over thesystem, the group average center frequencies of the L groups areselected and distributed to provide an average frequency sliding rate(per unit distance) for the solitons.

BRIEF DESCRIPTION OF THE DRAWING

A more complete understanding of the invention may be obtained byreading the following description of specific illustrative embodimentsof the invention in conjunction with the appended drawing in which:

FIG. 1 shows an exemplary soliton transmission system;

FIGS. 2 through 5 shows the relationship of the nominal filter centerfrequency to the transmission system length;

FIG. 6 compares the transmission curves for an exemplary etalon filterand a Gaussian filter with the spectrum for a soliton;

FIG. 7 compares the transmission curves for exemplary etalon filterpairs and a super-Gaussian filter with the spectrum for a soliton;

FIG. 8 shows the noise spectral density versus frequency, at variouspositions along a transmission medium with sliding-frequency guidingfilters, normalized to that density obtaining at 10 Mm with nofiltering;

FIG. 9 shows the normalized standard deviations of the soliton energy("ones") and of the noise in empty bit periods ("zeros") versus distancealong the transmission medium;

FIG. 10 shows the standard deviations in soliton arrival times versusdistance, for the sliding-frequency guiding filter arrangement of FIG. 1(dashed curves) and with no filtering at all (solid curves);

FIGS. 11 and 12 show exemplary embodiments of a soliton transmissionsystem employing plural groups of sliding-frequency guiding opticalfilters; and

FIG. 13 shows standard deviation in soliton arrival times versus thenumber of filters per group for the embodiments shown in FIGS. 11 and12.

DETAILED DESCRIPTION

For the description below, it is useful to define the term nominalcenter frequency as applied to filters. In the first instance, etalonsand other filter types may not have a response curve which lends itselfeasily to defining a center frequency because of a lack of 3 dB pointson the curve. In order to overcome this problem and handle potentiallyall filter types with a suitable term, the nominal center frequency of afilter is understood to be the frequency lying between the 3 dB pointson a frequency response curve raised to an arbitrary power greater thanunity which allows such 3 dB points to appear.

An optical fiber transmission system as shown in FIG. 1 includes atransmitter, a receiver and a transmission medium interconnecting thetransmitter and the receiver. Soliton pulses of optical radiation aregenerated at a nominal soliton center frequency Ω by transmitter 10. Thepulses are then coupled in the transmission medium which compriseslengths of optical fiber 11 and optical amplifiers and filters 12disposed at predetermined intervals along the transmission medium. Aftertransmission through the transmission medium, the pulses are thendetected at receiver 13.

Unidirectional transmission is depicted in order to simplify theexplanation of the principles of the present invention without limitingthe scope of the invention. This invention is applicable tobidirectional transmission systems. Moreover, the fundamental principlesof the present invention are described in terms of a single channel orsingle frequency soliton system. It will be briefly described hereinthat the principles of the present invention are extendible tofrequency-division-multiplexed systems utilizing a plurality ofdifferent soliton frequency channels.

Creation of soliton pulses is dependent upon proper launch andtransmission characteristics such as pulse power, pulse width, centerfrequency, fiber dispersion and the like. These characteristics are wellknown to those skilled in the art and will not be discussed furtherherein. For additional background information concerning solitongeneration and soliton transmission, see Optical FiberTelecommunications II, ed. S. E. Miller et al., pp. 90 et seq. (AcademicPress 1988) and see also U.S. Pat. No. 4,406,516.

The transmission medium covers an system path length L between thetransmitter and the receiver. In most systems of interest such astransoceanic or transcontinental systems, the system path length is atleast several thousand kilometers. Such long distance solitontransmission media are generally realized by a plurality of lengths ofoptical fiber 11 which are desirably single mode optical fibers havingthe appropriate group velocity dispersion for supporting solitonpropagation at frequency Ω and, as will be described below, at thosefrequencies caused by the action of the sliding-frequency guidingfilters. Silica-based optical fibers are suitable for this application.Fibers employing different materials as well as different propertiessuch as polarization preservation are contemplated for use herein.

Optical amplifiers and filters 12 are shown as a single element havingportions providing optical amplification and optical filtering. Inpractice, several elements such as separate amplifiers and filters maybe desired for realizing element 12. Each amplifier portion comprises anoptically pumped section of rare earth doped optical fiber to providegain to pulses propagating at the soliton center frequency. Eachfiltering portion comprises an in-line linear filter having a frequencydependent response characteristic defined around a nominal filter centerfrequency col. The filter response characteristic is selected to providea suitable amount of bandwidth limiting. Optical coupling elements mayalso be required to transfer the optical pulses to and from each opticalamplifier and filter 12. These elements are well known in the relevantart and have not been shown in the FIGs.

Optical filters are realizable from Fabry-Perot etalons, fiberFabry-Perot etalons and the like. Fiber Fabry-Perot etalon filters havebeen disclosed in U.S. Pat. No. 4,861,136, U.S. Pat. No. 4,830,451 andU.S. Pat. No. 5,037,180 which are expressly incorporated herein byreference. A multiport optical filter utilizing a Fabry-Perot etalon forwavelength selectivity is described in U.S. Pat. No. 5,050,954. Otherexemplary wavelength-tunable optical filters are described by H.Kobrinski et al. in IEEE Communications Magazine, pp. 53-63 (October1989), also expressly incorporated herein by reference. Etalons exhibitmany desirable characteristics such as tunability, appropriate shapingnear the response peak, and a periodic comb characteristic which, in thelatter instance, lends to their attractiveness forwavelength-division-multiplexing applications.

Optical amplifiers such as erbium-doped optical fiber amplifiers orRaman amplifiers are used in the system because they amplify the opticalsignals in the optical domain without requiring an opto-electronic orelectrooptic conversion in the process. Such amplifiers generallyrequire a pump source for generating the optical pump beam and a meansfor coupling the pump beam into the optical amplifying medium. Theseelements are not shown in the FIGs. When operating with the associatedfilters, it is desirable that each amplifier compensate the loss relatedto insertion of the associated filter.

Each optical filter in optical amplifier and filter 12-1 through 12-N isset to a nominal filter center frequency ω_(f),1 through ω_(f),N,respectively, wherein the nominal filter center frequencies areintentionally detuned from a reference frequency by some prescribed,varying amount. For example, the center frequency of the optical filtersmay be different from each other and from the nominal center frequency Ωof the soliton as it is launched into the relevant portion of thetransmission system. This allows for the use of stronger filters which,in turn, greatly reduces timing jitter problems in the solitontransmission system. The center frequency of each successive opticalfilter is translated up or translated down in a predetermined patternsuch as frequency increasing, frequency decreasing, and combinations ofboth. From the system point of view for a particular channel, theassociated filter frequencies are seen to be sliding with respect to anarbitrary reference frequency such as the launch frequency Ω of thesolitons. Thus, filters realized in accordance with the teachings hereinare now called "sliding-frequency guiding filters."

The use of the sliding-frequency guiding filters in optical amplifiersand filters 12 creates a transmission environment which is substantiallyopaque to noise while remaining perfectly transparent to solitons.Opacity to noise exists for all but a small fraction of the total systemlength. This will be described below with respect to FIG. 8. Analternative way of describing the transmission environment created byuse of the invention is that it permits solitons to leave behind, atsome fixed distance and in a different frequency band, the noiseemanating from the amplification process. In essence, the solitons areadiabatically and intentionally dragged away in the frequency domainfrom their related amplified noise. In this new transmission system,solitons are launched at a particular frequency Ω and, as they propagatealong the transmission medium, are accelerated toward successivelydifferent frequencies determined by each optical filter center frequencyω_(f),n (n=1, 2, . . . N) for the series of sliding-frequency guidingfilters thereby causing each soliton to emerge at a substantiallydifferent frequency from the launch frequency.

It should be noted that only the nonlinear (soliton) pulses can shiftfrequency along with the sliding-frequency guiding filters. The reasonfor this is that the nonlinear term in the propagation equation allowsthe soliton pulses to generate the new frequency components required forthe sliding. "Linear" pulses including noise, on the other hand, cannotgenerate the required new frequencies and hence eventually suffercatastrophic energy loss from the action of the sliding filters. Thus,the invention described here takes advantage of the fact that thesoliton pulses are nonlinear in a new and highly effective way.

For the initial portion of the description which follows, it is proposedthat all filters along the entire transmission medium exhibit thesliding-frequency guiding property. However, it is contemplated that theprinciples of the present invention extend to a system in which at leastsome relevant portion of the transmission medium includes two or moreoptical filters exhibiting the sliding-frequency guiding property. Forexample, it may be desirable to shed dispersive wave radiation viasliding-frequency guiding filters in the initial portion of the systemtransmission medium while having standard filtering in the remainingportion of the transmission medium. Alternatively, it may be desirableto follow a transmission medium section of positive sliding as in FIG. 3with a transmission medium section of negative sliding wherein thefilter center frequencies decrease over distance.

It is important to distinguish the intentional nominal center frequencytranslation of the inventive sliding-frequency guiding filters from theprior art filters designed with a substantially identical nominal centerfrequency yet exhibiting small frequency deviations resulting fromunintentional manufacturing defects or manufacturing tolerances. In thecase of sliding-frequency guiding filters depicted in FIGS. 3-5, theamount of frequency translation for soliton pulses over the relevantportion of the system is a significant fraction of the solitonbandwidth. That is, |ω_(f),N -ω_(f),1 | is at least of the order of0.5•B_(sol) (B_(sol) is the soliton bandwidth). When compared with thesoliton bandwidth, the frequency differences for the prior art filtersin soliton transmission systems as depicted in FIG. 2 are such thatsolitons emerge from the system at substantially the same frequency withwhich they were launched. That is, |ω_(f),N -ω_(f),1 | is approximatelyzero. For the latter case, the prior art systems utilize substantiallyidentical filters along the transmission medium. But, the substantialidentity of the filters is observable only within manufacturing limits.

When employing the sliding-frequency guiding filters as taught herein,stronger filter response characteristics are employable therebyachieving greater jitter reduction than prior art systems withoutincurring the usual penalty of exponentially rising noise from theexcess amplifier gain required to overcome the additional filter loss.The strength of the filter response is a function of the curvature ofthe filter response peak. Strong filtering is generally associated withsharp cutoff frequencies and high quality (Q) factors.

Exemplary transmission media exhibiting principles of thesliding-frequency guiding filter invention are shown in FIGS. 3-5. InFIG. 3, the nominal center frequency of each successive filter along thetransmission medium increases monotonically with distance. It iscontemplated that the nominal center frequencies of consecutive filterscan decrease monotonically with distance.

In FIG. 4, the nominal center frequencies of consecutive filters arestaggered in an alternating pattern around a straight line. Such staggertuning allows for a cumulative filter transmission shape, attained byconsecutive filters such as ω_(f),1 and ω_(f),2, for example, which isflatter near the peak and has steeper sides. This altered filtertransmission shape in turn allows for stronger guiding of the solitonpulses and greater jitter reduction for a given soliton energy loss.Equivalently, it allows a reduced loss and hence for reduced build-up ofnoise for a given degree of guiding.

In FIG. 5, each filter is shown to comprise two filters at the samenominal center frequency to create overcoupling and, thereby, a strongerfilter response as shown by curve 25 in FIG. 7.

While FIGS. 3-5 show substantially equal detuning amounts between thecenter frequencies of consecutive filters (FIGS. 3 and 5) or alternatefilters (FIG. 4), it is contemplated that different or unequal detuningamounts can be employed for the filters along the transmission medium.In other words, the frequency difference between center frequencies ofadjacent filters need not be equal for the entire transmission medium.Moreover, the spacing of filters need not occur at regular, periodicintervals nor in conjunction with each and every amplifier. Irregularfilters spacings are contemplated within the principles of the presentinvention.

For the transmission media shown in FIGS. 3-5, the rate of change ofnominal center frequency detuning as a function of distance is less thana prescribed maximum. If the maximum rate were exceeded, then amplitudeand frequency fluctuations would create an unstable condition leadingeventually to the elimination of the soliton pulses. For a parabolicallyshaped filter peak response, the exemplary maximum rate has beendetermined to be approximately (2/27)^(1/2) η, where η describes thecurvature per unit soliton length of the parabolically shaped filterresponse around the peak at the nominal center frequency. Typically, theresults of such instabilities are seen over distances on the order ofthe soliton unit distance, z_(c).

The following description provides the presently understood theoreticalbasis underlying this invention. Also, examples from experimentalsimulations are included to show the performance of a solitontransmission system including the sliding-frequency guiding filters.

The propagation equation for solitons, including filter loss andcompensating gain from the amplifying elements, is: ##EQU1## where α andη are the excess gain and filter peak curvature, respectively, per unitlength and where cot is the nominal peak or center frequency of anoptical filter per unit length. Although the quantities α and η arecharacterized as continuously distributed quantities, it will be shownimmediately below that they are easily converted into lumped, periodicequivalent quantities consistent with the use of lumped periodicamplifying and filtering elements 12.

The propagation of solitons in a fiber is most conveniently described interms of a differential equation, the nonlinear Schrodinger equation.All quantities in the equation are treated as continuously distributed,and many parameters are typically considered constant as well. Yetrealizable systems tend to involve quantities that have significantperiodic variation such as the soliton pulse energy while many otherssuch as amplifiers and filters are at the extreme of such variation,i.e., they are "lumped". When the periods in question are short enoughrelative to the soliton unit distance, z_(c), lumped quantities can beconverted into their continuously distributed equivalents, and all otherperiodically varying quantities replaced by their path-averageequivalents. Then the real system behaves remarkably like itscontinuously distributed equivalent.

In particular, in the theoretical treatment of soliton propagationthrough a set of guiding filters, the filter effect is regarded ascontinuously distributed. The quantity η is the curvature of the filterresponse, at its peak, per unit length along the transmission medium.More precisely stated, for a small enough distance dz, the transmissionfactor T at the frequency ω, for filters with resonance peak at ω_(f),is,

    T(ω,dz)=1-[η(ω-ω.sub.f).sup.2 dz].   2

Since the transmission factor over a finite distance z is the product ofthe factors given by EQ. 2, the logarithm of that factor is just the sumof the logarithms of EQ. 2. Making use of the fact that ln (1-ε) =-ε for|ε|<<1, one then has: ##EQU2## By realizing lumped filters with acurvature η_(f) and a constant spacing L, where L is short relative toz_(c), the correspondence between the continuously distributed η oftheoretical work and the η_(f) of the practical lumped filters issimply,

    η.sub.f =ηL.                                       5

Consistent with the description above, it is possible to write thetransmission factor of an individual lumped filter as

    T(ω)=exp[-η.sub.f (ω-ω.sub.f).sup.2 ]6

Most practical filters such as the etalon, for example, have atransmission factor which is in general significantly different fromthat of EQ. 6, except for a region near the filter peak. Fortunately,however, one can show that the practical lumped filters guide solitons(dampen their amplitude and timing jitters) almost the same as thecontinuous filters of EQs. 2 and 3, as long as they have essentially thesame behavior near their peaks, that is, as long as the transmission ofthe practical filter is essentially parabolic near its peak and as longas EQ. 5 is satisfied. The transmission function of an etalon is,##EQU3## where R is the common reflectivity of the etalon mirrors, whereδf is the frequency difference, in practical units, corresponding toω-ω_(f), and where the free spectral range (separation between adjacentresonance peaks) of the etalon, Δf, is given by ##EQU4## where d is the(air) gap between mirrors. By expanding EQ. 7 about δf=0, one can easilyshow that the etalon's peak curvature, referred to the practicalfrequency difference (δf), is ##EQU5##

In theoretical work, unless otherwise indicated, instead of thepractical units of meters, seconds, Gigahertz, etc., it is possible touse the special soliton units z_(c), t_(c), and ω_(c), respectively. Thesoliton unit length, z_(c), is a characteristic length for dispersiveeffects, and is given by ##EQU6## where c is the vacuum speed of light,λ the wavelength, τ the full-width at half-maximum (FWHM) bandwidth ofthe soliton, and D is the optical fiber group delay parameterrepresented in units of time/unit wavelength-shift/unit length. Withinthe context of ultra long distance soliton transmission, z_(c) istypically at least many hundreds of kilometers long. The soliton unittime, t_(c), is ##EQU7## where τ is the full width at half maximum ofthe soliton pulse. Finally, the soliton unit frequency, ω_(c), is oneradian per t_(c). Thus, the frequencies ω, in soliton units, areconverted to practical frequencies, as ##EQU8##

In an example of sliding-frequency guiding filters to be discussed inmore detail below, it is assumed that τ=20 psec and D =0.4 psec/nm/km,so that (by virtue of EQ. 10) z_(c) =250 km, and (by virtue of EQ. 12)ω_(c) corresponds to 14.0 GHz. It is also assumed that η=0.6 (per ω_(c)2 and per z_(c)). Thus, in practical units, η becomes ##EQU9## If thereis one filter every 30 km, then from EQ. 5,

    η.sub.f (GHz.sup.-2)=30×1.2245×10.sup.-5 =3.6735×10.sup.-4.                                  14

In order to obtain this filter strength from etalons having a freespectral range (WDM channel spacing) Δf=100 GHz (Δλ=0.8 nm at λ≈1550nm), from EQ. 10 it is known that the etalons must have a spacing d=1.5mm. Putting the η_(f) and Δf we have just calculated into EQ. 9, oneobtains R=0.0930 (1-R)², and solving, one obtains R=0.0789. FIG. 6 showsthe transmission curve for such an etalon (curve 22), compared with thatof the corresponding Gaussian frequency response spectrum (curve 23) andwith the frequency spectrum of the 20 psec wide soliton (curve 21). Thestrength of the filtering is best judged from the cumulative effect overone soliton unit distance (z_(c)).

By way of further comparison, FIG. 7 shows the transmission curves for apair of non-staggered etalons (curve 26) as shown by each filter pair inFIG. 5, a pair of staggered etalons (curve 25) as shown by a pair ofadjacent filters in FIG. 4, and a super-Gaussian frequency responsespectrum (curve 24) compared with the frequency spectrum of the 20 psecwide soliton (curve 21).

Prior art systems which are characterized as being withoutsliding-frequency guiding filters are described as having dω_(f)/dz≡ω_(f) '=0 where z is distance in terms of the system length. Forconvenience, ω_(f) is set to zero which allows the exact stationarysolution to EQ. 1 to be found as: ##EQU10## where 100 =Kz-ν ln cosh(t)and where the parameters α, η, P, and ν satisfy the followingrelationships: ##EQU11## The parameter P indicates soliton amplitude(power) while the parameter ν involves frequency chirp. From EQ. 15, thefrequency of a soliton pulse is chirped so that ∂φ/∂t=-ν tanh(t).Because of this chirp, both the bandwidth and the time-bandwidth productof the soliton pulse are increased by the factor (1+ν²).

By numerical simulation, we have been able to show that use of theinventive sliding-frequency guiding filters, within certain limits givenbelow, does not significantly alter this solution. The use ofsliding-frequency guiding filters does, however, alter the damping ofamplitude and frequency fluctuations for the soliton pulses. Toinvestigate the damping with sliding, the general form for the solitonis introduced into EQ. 1 as u=A sech(At-q) exp(-iΩt +iφ). The followingpair of coupled, first order perturbation equations are obtained asfollows: ##EQU12## where ω_(f) (z) is the frequency of the filter peakat distance z along the transmission medium. Equilibrium at A=1 and atconstant ω_(f), requires that the soliton frequency Ω lag behind thefilter frequencies by an amount ##EQU13## This frequency offset furtherincreases the loss from the filter because the soliton pulse ispositioned on a negative or positive slope of the filter responsecharacteristic. As a result, the excess gain α must increase as follows:##EQU14## This value of α is then inserted into the EQs. 19 and . 20 Inorder to understand more clearly how fluctuations are damped by thesliding-frequency guiding filters, it is useful to introduce smallfluctuation parameters α and Δ into the relationships for A and Ω asfollows: A=1+α and Ω=ω_(f) -(3ω'_(f) /2η)+Δ. By linearizing theequations with respect to the small fluctuations, we obtain thefollowing coupled equations: ##EQU15## By letting the derivatives inEQs. 23 and 24 have the common value -γ, we can decouple the equationsand obtain the normal modes: ##EQU16## where the corresponding decayconstants γ₁ and γ₂ are given as: ##EQU17## For stability, both γ₁ andγ₂ must remain positive. This, in turn, sets a maximum allowable slidingrate for parabolically shaped filter response peaks as follows:##EQU18##

For brevity, we merely quote the results of our computation of thevariances in soliton energy and arrival time. The normalized variance insignal energy is, ##EQU19## where N is the spontaneous emission noisespectral density generated per unit length of the transmission medium.For γz>>1, the variance comes to an equilibrium value ##EQU20## whereγ_(eff) is given by, ##EQU21## For the prior art case of no slidingfilters, the damping constants are equal, γ₁ =γ₂ =γ_(eff), as required.

The reduction factor for the variance of the timing jitter experiencedfrom the use of the sliding-frequency guiding filters along thetransmission medium is given by, ##EQU22## where the f_(ij) (z) aregiven by, ##EQU23## Here, for γz>>1, ##EQU24## where γ_(eff) is nowgiven by, ##EQU25## Finally, it should be noted that EQs. and yield thef(x) of EQ. 28 of the Optics Letters paper by Kodama, supra, describingthe prior art transmission system having no sliding-frequency guidingfilters, that is, when γ₁ =γ₂.

Noise reduction and the other practical benefits accruing from the useof sliding-frequency guiding filters are described in relation to aspecific example below. Consistent with a single-channel rate of 10 Gbpswith commonly polarized soliton pulses, or with 20 Gbps when neighboringpulses are orthogonally polarized, the soliton pulse width (FWHM) τ isassumed to be approximately 20 psec. The assumed pulse width whencombined with a group velocity dispersion for optical fiber 11, D=0.4ps/nm/km, yields roughly the same soliton pulse energy reported in ourrecent article at Electronics Letters, Vol. 28, p. 792 (1992), where thesafety margin against energy errors was about a factor of two at 10 Mm.Consequently, the soliton unit distance z_(c) is approximately 250 km ata transmission wavelength λ of approximately 1556 nm. Consistent withthe jitter reduction we wish to achieve, yet just small enough not topush the limits of first order perturbation theory too hard, we chosethe filter curvature parameter η=0.6--a filter strength value about 7.5times larger than reported in any prior art experiment. To prevent thereduction factor in standard deviation of jitter (the square root of EQ.32) from becoming no more than about 1.5 times its value with no slidingfilters, we make ω'_(f) =η/6=0.1 which is approximately 0.6 max(ω'_(f)).Since here the soliton frequency unit is equivalent to 14 GHz, thesliding rate represented in practical units is 5.6 GHz/Mm. Thus, thetotal frequency translation over the entire transmission path of 10 Mmis only 56 GHz, or just slightly more than three soliton bandwidths,B_(sol). Finally, to compute the excess gain α correctly, EQ. 22 ismodified to include effects of the bandwidth factor 1+ν² as in EQ. 17:##EQU26## It should be understood that α is proportional to the rate atwhich noise grows in the system. From 1+ν² =1.132 and the values of ηand ω'_(f) given above, EQ. 35 yields an excess gain per unit distanceα=0.244.

To compute the noise spectrum shown in FIG. 8, it is necessary to sumthe noise contributions generated in each segment of the transmissionmedium as modified by the appropriate excess gain factor and by theaccumulated loss of the frequency-sliding, guiding filters. For example,when the filter transmission functions are represented byexp(-η(ω-ω_(f))²), the noise spectral density (noise power per unitbandwidth) at distance z, as normalized to the noise spectral densitywhich would obtain at the total system length L with no filtering, is,##EQU27## FIG. 8 shows N(ω,z) as computed numerically for the particularparameters of the example, essentially according to EQ. 36, except thatactual Lorentzian filter functions were used. Each curve in FIG. 8 islabeled to denote the noise spectral density curve at a particulardistance z in Mm along the transmission medium. Moreover, the curves arenormalized to the density achieved at 10 Mm for a transmission systemwithout the sliding filters, that is, with conventional identicalfilters. After about 5 Mm, the peak spectral density saturates at a veryacceptable level which is slightly greater than 2.0. In the prior artsystems without sliding-frequency guiding filters, the peak noisespectral density would have risen at an exponential rate, by nearly e¹⁰˜20,000 times!

In FIG. 9, normalized standard deviations of the soliton energy ("ones")and normalized standard deviations of the noise energy in empty bitperiods ("zeros") are plotted against distance z. Curves labeled withthe number "1" relate to soliton energy while curves labeled with thenumber "0" relate to noise energy. These curves are obtained from EQ.28, data in FIG. 8, and analysis described by us in J. LightwaveTechnology, 9, p. 170 (1991). The solid curves represent a systemwithout sliding-frequency guiding filters; the dashed curves representthe same system with sliding frequency guiding filters. Fiber loss isassumed to be 0.21 dB/km and effective core area of the optical fiber isassumed to be 50 μm². Amplifier spacing and excess spontaneous emissionfactor are 28 km and 1.4, respectively. With sliding filters, bothstandard deviations ("0" and "1") soon become clamped to small, constantvalues which correspond to immeasurably small bit error rates.

In FIG. 10, the standard deviation in timing jitter is plotted versusthe path length. Approximate effects of the acoustic interaction areincluded as described in Soviet Lightwave Communications, 1, p. 235(1991), but as modified by our own experimental measurements describedin the Electronics Letters article cited above. The effects are plottedfor several different bit rates, 0, 10, and 20 Gbps where 0 Gbpsrepresents the pure Gordon-Haus effect described earlier. Solid curvesrepresent system performance without the sliding filters while thedotted curve represents the system performance with sliding filters. Forexample, at a distance of 10 Mm, the standard deviation in timing jitterfor the sliding filter system is approximately 2 psec, which is suitablefor error-free transmission at 20 Gbit/s or more per channel, ascompared with a standard deviation of 15 psec for the system withoutsliding filters. Clearly, error-free transmission of higher bit-ratesoliton channels is achievable through the use of sliding-frequencyguiding filters.

The sliding-frequency guiding filter approach described above canundesirably burden system designers and manufacturers by requiring asignificant number of individually tuned optical filters for the entiresoliton transmission system. For example, in a transoceanic systemrequiring 30 km spacing between adjacent filters, the entire 9,000 kmsystem requires installation of approximately 300 individually tunedfilters. In order to alleviate this problem and as an alternativeimprovement to the invention described above, I have discovered that thesuperior transmission environment afforded by the sliding-frequencyguiding filters can be maintained in a system where the N×L opticalfilters are arranged so that N consecutive filters are designated to bein one of the L filter groups along the soliton transmission system.

Optical filters in a particular filter group have their nominal centerfrequencies combined to form a group-average center frequency for thatgroup. The group-average center frequency for a group differs from thegroup-average center frequency for the other groups. Over the system,the group-average center frequencies for the plurality of groups areselected and distributed along the system to provide an averagefrequency sliding rate for translating the solitons. The averagefrequency sliding rate is measured in units of frequency per unitdistance.

While it is preferred that the separation between adjacent filters beuniform, it is anticipated that distribution of the optical amplifierand filter elements 12 may result in a non-uniform separation betweenadjacent filters in a group or between adjacent groups. In thedescription which follows, the embodiments of this invention utilizesubstantially uniform separation between adjacent filters.

In FIG. 11, a soliton transmission system is shown employing pluralgroups of sliding-frequency guiding optical filters wherein each groupcomprises filters tuned to a substantially identical optical nominalcenter frequency. That is, the optical filters depicted in group 50-1are set to substantially the same optical frequency. Similarly, thefilters in group 50-2 are set to the same optical frequency. As aresult, the group-average center frequency for a particular group offilters is substantially equal to the nominal center frequency for eachfilter in the group. It should be noted that each of the groups exhibitsa different group-average center frequency than the other groups. Butwhen viewed across the transmission system, the group-average centerfrequencies of the groups establish an average frequency sliding ratefor the system so that the solitons are accelerated from one frequencyto the next while maintaining their soliton properties. The averagesliding rate is approximated in FIG. 11 by the slope of the solid linewhich represents the average frequency of solitons propagating along thesystem.

The example shown in FIG. 11 is for a simulation in which each groupcomprises 40 optical filters having a 30 km separation between adjacentfilters. Each filter is a Fabry-Perot etalon with a free spectral rangeof approximately 100 GHz and reflectivity of approximately 0.081. Thereis substantially no standard deviation among the nominal centerfrequencies for the optical filters in a particular group. By creating afrequency gap of 6.72 GHz between adjacent filter groups, it is possibleto establish an average sliding rate of 5.6 GHz/Mm across the solitontransmission system. In a 9,000 km transoceanic system, the group sizeand filter separation result in a need for only eight different groupsto span the distance. As the number of filter groups is decreased for agiven length system, the frequency gap between adjacent groups isincreased in order to maintain a comparable average frequency slidingrate. This, in turn, causes the solitons to suffer an increased loss. Asthis added loss is off-set by increasing the gain of optical amplifiersalong the system, there will be a concomitant increase in the jitterexperienced by solitons. While system designers may opt the smallestpossible number of filter groups in a particular soliton transmissionsystem, it should now be understood that a decrease in the number offilter groups is counteracted by an increase in the amount of jitterexperienced by the solitons.

An evaluation of jitter as a function of the number of filter groups wasperformed by computer simulation for the system shown in FIG. 11. Theresults of this evaluation are depicted in the data points marked by an"x" in FIG. 13. This simulation assumed a system length of 9,000 km, asystem transmission rate of 10 Gbps, and a soliton pulse width ofapproximately 20 ps. The results shown in FIG. 13 reveal that theassumed soliton transmission system introduces an almost negligibleincrease (0.2 ps) in jitter relative to the system shown in FIG. 3 wheneight filter groups are employed using approximately 40 filters pergroup.

It is understood that imperfections may occur in the tuning ofindividual filters to a nominal center frequency established for agroup. Such contemplated imperfections are depicted in FIG. 12 whereinthe L filter groups 51 each show a random distribution of their filters'nominal center frequencies. In FIG. 13 and in the simulation performedfor the system depicted in FIG. 13, a Gaussian distribution wasestablished for the nominal center frequencies of the filters in aparticular group. It is contemplated that other distributions such asuniform, Rician, and the like may be suitable random distributions.

FIG. 13 shows the results of a simulation of a soliton transmissionsystem identical in all but one respect to the system described above.The singular difference in this case is that the nominal centerfrequencies for the filters in a particular group are randomlydistributed around an ideal center frequency. The points represented bydots relate to the case where the standard deviation of the filternominal center frequency distribution is approximately 4.0 GHz; and thepoints represented by squares relate to the case where the standarddeviation of the filter nominal center frequency distribution isapproximately 5.0 GHz. These results reveal that as long as the standarddeviation of the filter nominal center frequency distribution within afilter group is smaller than 5 GHz for the assumed system, there will beonly a small increase in soliton jitter resulting from this imperfectfilter tuning.

Sliding-frequency guiding filters and their filter groups bring severalother important benefits to optical soliton transmission systems. First,they make the system performance much less sensitive to defects in theinput pulses. In a system without sliding filters, the dispersive waveradiation shed by imperfect pulses always remains in the same frequencyband with the solitons, and hence can add significantly to the noise.However, with strong, sliding-frequency guiding filters, such noisetends to be generated entirely in the first fraction of a Megameter ofthe transmission medium, so that the sliding filters can completelyremove the noise long before it reaches the receiver. Second, a similar"cleaning" effect applies to another potentially important source ofnoise, viz., the dispersive wave radiation shed by the solitons as theyreact to polarization dispersion. Third, the use of sliding filtersshould enable a great reduction in the number of isolators required tosuppress the build up of noise from Rayleigh double backscattering. Atmost, only a handful of isolators would be required to be locateddesirably near the output end of the system, if at all. Fourth, strongdamping constants permitted by sliding filters greatly reduce thevarious penalties of wavelength-division-multiplexing (WDM), such asfrom soliton-soliton overlap at the system input. Finally, strongfilters substantially help with the problem of equalizing signalstrengths among channels.

Soliton sliding filters have been described above here using onlysimple, passive, polarization-independent devices which are fullycompatible with extensive WDM. By contrast, filtering in the time domainrequires active devices, with all the same drawbacks of complexity,reduced reliability, high cost, and incompatibility with WDM thataccompany electronic regeneration.

It is understood that the description above relied on aparabolically-shaped filter response characteristic in order to simplifythe explanation of the principles of this invention. Theparabolically-shaped response offers a useful ratio of damping (foramplitude and phase variations) to loss. In practice, it is contemplatedthat any realizable filter response characteristic shape may beemployed. For example, a strong, square-shaped response characteristicis expected to yield superior results. Other filter strength and slidingrate characteristics have been described in my co-pending U.S. patentapplication Ser. No. 08/297,336 (Mamyshev-Mollenauer Case 2-31) filed onAug. 29, 1994, which is expressly incorporated herein by reference.

What is claimed is:
 1. A lightwave transmission system supportingsoliton propagation in a particular band of frequencies and comprisingan optical fiber transmission medium including both a plurality ofoptical amplifiers spaced apart along the optical fiber transmissionmedium and a plurality of optical filters spaced apart along the opticalfiber transmission medium, the lightwave transmission systemCHARACTERIZED IN THAT,the plurality of optical filters is organized intoa plurality of filter groups, each filter group comprising at least Nfilters where N is an integer and N≧2, each filter group exhibits agroup average center frequency which is different from the group averagecenter frequency of each other filter group, the plurality of filtergroups together exhibit an average frequency sliding rate for moving thefrequency of the soliton toward each filter group's group average centerfrequency, each group average center frequency being in the particularband of frequencies.
 2. The lightwave transmission system as defined inclaim 1 wherein each optical filter in a filter group exhibits a nominalcenter frequency substantially equal to the nominal center frequency ofeach other optical filter in that filter group.
 3. The lightwavetransmission system as defined in claim 1 wherein each optical filter ina filter group exhibits a nominal center frequency and wherein thenominal center frequencies for optical filters in the same filter groupexhibit a random distribution about said group average center frequencyassociated with the filter group.
 4. The lightwave transmission systemas defined in claim 1 wherein the group average center frequencies ofthe plurality of optical filter groups increase substantiallymonotonically as a function of distance over the length of thetransmission medium.
 5. The lightwave transmission system as defined inclaim 1 wherein the group average center frequencies of the plurality ofoptical filter groups decrease substantially monotonically as a functionof distance over the length of the transmission medium.
 6. The lightwavetransmission system as defined in claim 1 wherein, over at least aportion of the transmission system, the group average center frequenciesof the plurality of optical filter groups change from a first frequencyto a second frequency at an average frequency sliding rate less than orequal to approximately (2/27)^(1/2) η, where η describes curvature perunit soliton length of a parabolically-shaped filter response around thenominal center frequency.
 7. The lightwave transmission system asdefined in claim 1 wherein the plurality of filter groups adiabaticallytranslate the solitons along the transmission medium from a firstfrequency to a second frequency different from the first frequency sothat the solitons are separated in frequency from noise generated by theamplifying means and wherein a magnitude of the difference between thefirst and second frequencies is greater than or equal to one-half thebandwidth of the soliton.